Statistics is the science which deals with the collection, the analysis, the visualization and the interpretation of experimental data.
Statistics
How data are collected …
- Random samplings
- Observational studies
- Experiments
Random Samplings (polls)
⚠️ Definition:
Random samplings allow to characterize the properties of a finite population without measuring all of its members.
Examples
- Electoral polls
- Normal levels of cholesterol in the human population
- Characterization of a population of grapes, apples, wines, …
- …
Observational Studies
⚠️ Definition:
Observational studies are designed with the objective of identifying relationships between the different properties of a conceptual population. The role of the experimenter is to perform the selection of the sample.
Examples
- Is it true that people who eat more chocolate are more happy?
- The level of cholesterol of people eating more vegetables is lower …
Experiments
⚠️ Definition:
Experiments are designed with the objective of identifying causal relations between the properties of a conceptual population. The role of the experimenter is to modify the conditions to verify the presence of causal relationship between the observed properties.
Examples
- If you eat more chocolate you will get happier
- If I drink more beer I’ll get more sympathetic
- …
Important notes
Causal relations can be assessed only in experiments
This is really Galileian ;-)
Experiments are impossible in many relevant fields like human health and ecology
Should we then give up on obtaining causal information there?
Mind the chocolate …
New England Journal of Medicine, 2012
” … Chocolate consumption enhances cognitive function, which is a sine qua non for winning the Nobel Prize, and it closely correlates with the number of Nobel laureates in each country …“
Planning a sampling
⚠️ Key question
What is the best way to sample my population in a representative way?
- Do it randomly to avoid any intentional or unintentional bias (Randomized Sampling)
- Take into account known subpopulations and confounding factors (Stratified Random Sampling)
- The number of samples is determined by practical/economical considerations
In presence of known subpopulations stratified random sampling results in a more accurate characterization of the population
Stratified Random Sampling
Key idea: do it randomly
The most reasonable way to “smear out” the effects of unknown biases is to do everything randomly
Random is not a synonym of HAPHAZARD
Planning an observational study
Objective: get an useful and clear answer.
Mean: start from a clear, useful and often simple question.
- Identify the sampling unit
- Decide the number of samples (money, power, …)
- Define the conceptual population
- Sample it in a representative way
- Identify confounding factors and, if possible, stratify for them
Key idea: Sampling Unit
The smaller unit of a population which retains the properties we are interested into
- Example: grapevine, leafs, infections …
Key idea: Confounding Factor
A variable that influences both the dependent variable and independent variable, causing a spurious association (wikipedia).
- Smoke, cardiovascular disease, alcohol consumption
- Birth order (1st child, 2nd child, etc.), maternal age, Down Syndrome in the child
Notes
- Some confounders can be controlled by careful sampling
- Eg. Age and Gender on the relation between happiness and chocolate
- Some others are impossible to control
- Eg. Presence of chemical pollution in the water streams and altitude of sampling
Planning one experiment
Objective: get an useful and clear answer.
Mean: start from a clear, useful and often simple question.
- What is my experimental unit?
- How many samples should I measure?
- What are the potential sources of variability?
Experimental Design
⚠️ Definition
A strategy to assign the experimental units to the different treatments to optimize my capacity of inferring causal relationships
Control of unwanted sources of variability (technical/biological) to highlight the effects of the intervention
Key tool : Blocking
- Group experimental units in homogeneous groups (blocks)
- Study the variability inside the blocks
- Identify and subtract the variability across the blocks
- Blocking allows to subtract the difference between the blocks
- Blocks and study factors should be orthogonal
Block what you can; randomize what you cannot …
Examples of common blocking factors
- Location
- Analytical batch
- Day
- Operator
- …
Randomized Complete Designs
Split Plot Designs
Longitudinal Studies
Crossover Studies
Notes
Notes
Block as much as possible!
Repeated measures are more “powerful” because each unit is the control of itself
Crossovers can be tricky for the wash-out
Repeated measures design are the key in presence of large variability in the population (e.g. plants in the field/greenhouse)